But Mr Gove’s pivotal role in leading the successful Leave campaign means he could also follow other Brexiteers out of Cabinet over concerns about its impact.

Mrs May lavished praise on the Environment Secretary as she fielded questions over whether he was being lined up to replace Dominic Raab, who dramatically quit over the withdrawal agreement.

Mr Gove pulled out of an agricultural event in York today for family reasons and remained tight-lipped when he was tracked down by broadcasters later.

Mrs May created the Department for Exiting the European Union (Dexeu) to handle negotiations with Brussels after the 2016 referendum.

But the only two Cabinet ministers to have led it, David Davis and Mr Raab, both quit in frustration at the Prime Minister’s ultimate control over the exit deal and proposals for future trading relations.

Mr Davis walked out in July saying he could not support the Chequers blueprint for future relations with the EU just days after attending the Cabinet summit where it was signed off.

Mr Raab quit in similar circumstances, writing a letter to the PM the morning after the draft divorce deal was formally agreed following hours of discussions by senior ministers.

The Prime Minister has insisted the agreement struck with Brussels is the best that can be reached and delivers on Brexit.

After a wave of resignations in protest over the details of the plan and plots by Tory backbenchers to oust her, Mrs May faced reporters at a press conference in Downing Street.

Asked if she was struggling to fill the gaps in her ministerial team, the PM said she had had “rather a busy day” so had not finalised the new appointments.

She added: “Michael has done an excellent job at Defra, particularly in his defence of the fishing industry.

“There are some very important elements of the outline political declaration which recognise the UK will be an Independent Coastal State in the future.

“Fishing is an issue that matters to people and Michael has been doing an excellent job in ensuring we are delivering on that commitment that we have to come out of the Common Fisheries Policy.

“I have not yet appointed a new Dexeu Secretary and I will of course be making appointments to the Government in due course.”